If we consider the discretised form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling. A special treatment is required in order to velocity-pressure coupling. The methods such as:
provide an useful means of doing this for segregated solvers. However it is possible to solve the system of Navier-Stokes equations in coupled manner, taking care of inter equation coupling in a single matrix.
we have at each cell descretised equation in this form,
For continuity :
so we get:
this gives us:
from this a pressure correction equation could be formed as:
This is a poisson equation.
Here the gradients could be used from previous iteration.
See SIMPLE algorithm
See PISO algorithm